A few notes on the squirrel thing: I have squirrel issues with my nut trees, but not a lot in the fruit. Usually there are enough acorns and bay nuts to keep them busy, but I suspect I’ll have more trouble in the future. But, I go out of my way to hunt squirrels to eat. If well prepared they are very good eating and easy to prepare, especially if you don’t want to keep the skin. The skin, at least of our Western Gray Squirrels, is not only the perfect size and consistency to learn tanning leather, but the skin is very nice. Sure it’s small, but it’s quality skin and thick enough to make small items. I tell people all the time if you want to learn to tan, learning on squirrel skins is great, either for hair off, or hair on tanning. If you don’t want the skin, look on youtube and there are a bunch of guys who will show you how to skin them very fast and clean by cutting the skin in half. They are very easy to process. This guy says he can do them in 30 seconds or less. https://www.youtube.com/watch?v=FtspCxIfWuI I realize that to many modern Americans, eating squirrels, let alone going out of your way to hunt them would be considered strange behavior, but millions of Americans still think it doesn’t get any better than hunting and eating squirrels and that’s how it’s always been. Strange times we live in 
I hunt them almost exclusively with a .22 caliber air rifle. This is not a toy, but an accurate deadly tool if your aim is good. It is quieter and safer than a regular .22 rifle and the pellets are cheaper than bullets. It is also light. A scope is almost essential, unless you can get very close, and in any case will reduce the incidence of injured escaped squirrels and allow you to shoot farther and get more squirrels. A good air rifle isn’t that cheap by the time you put a decent scope on it, but they are fun to shoot and you can also take other game and pests with it. I’ve taken a lot of wild turkeys with mine and also used it to dispatch wiley chickens. The Chickens quickly learned that once the rifle came out, one of them was going to be lunch and they would all run off and hide immediately. If you have invasive pest birds, like starlings, it is a relatively safe, effective way to dispatch a few in many situations. I have a silencer on mine, so it probably sounds something like a loud nail gun.
A very effective way to take squirrels is with nooses along a pole. It is not legal here and probably not in many areas, but probably okay anywhere trapping squirrels is legal. Check your game laws. copper wire nooses are attached to a pole that runs from one tree to another. If you run a pole from any tree to another tree or to a fence, or to the ground etc, squirrels will go out of their way to use it. The nooses have to be set just right so that they just fit the head of a squirrel running, without catching the feet. They think nothing of the wire, because they are used to running through twigs anyway. You can set several along one pole and if they run past one, they might get caught in one of the others. If you set them right, the squirrel will be caught be the neck, jump off and be killed by hanging. The disadvantages are that if you catch a leg or two the squirrel will suffer a long time. Also, it’s not the greatest way to die in the first place and there are probably traps that make for a quicker kill. The advantage is that catch of non-target animals like birds should be very, very low since they are very specific to how the squirrel behaves. They are also cheap. These snares are pretty much invisible to the squirrel as a threat, so there is no fear or suspicion to overcome. Finally, they take advantage of a very predictable squirrel behavior. You can set up a pole permanently in a domestic situation and know almost without fail that every squirrel that moves in will use the pole. This would be an excellent way to take pestilent city squirrels with almost no chance of catching non-target animals unless they are other species of squirrels. Since there is no bait, other animals, namely birds which are common as by-catch in rodent traps of most kinds, won’t be tempted near the trap. Setting the nooses can be somewhat tricky. Watch a squirrel run along a pole and set the noose just high enough not to catch the feet and just big enough to take the head. Here is a video I made of a squirrel running on a pole https://youtu.be/k6Vfg3EHQMk?t=3m26s The wire has to be thin enough to close easily and heavy enough to support the weight of the squirrel easily. I can’t remember what gauge I used, its been a long time since I set any. With any trapping, checking your traps frequently is the decent thing to do. No matter how careful, by catch, body snares and other unpreferable things happen and you can avoid some suffering by frequent checks. Traps like leg hold, conibear and ground snares are especially prone to by-catch.
